PSCA-CAR T Cells in Treating Patients With PSCA+ Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: * All participants must have the ability to understand and the willingness to sign a written informed consent * Eastern Cooperative Oncology Group (ECOG) performance status 0 - 2 or KPS ≥70%. * Documented castration resistant prostate cancer (mCRPC) (Note: castration will be defined by a testosterone \< 50 ng/dL achieved by orchiectomy or luteinizing hormone-releasing hormone \[LHRH\] agonist/antagonist therapy) * Documented PSCA+ tumor expression as evaluated by City of Hope (COH) Pathology Care * Progression of disease manifest by one of the following means during treatment with at least one advanced androgen targeted therapy (e.g., abiraterone or enzalutamide) * Rising PSA documented on 2 occasions at least 7 days apart, with absolute increase \> 2 ng/dL despite testosterone \< 50 OR * Radiographic evidence of new metastatic foci on computed tomography (CT) or bone scan, or soft tissue progression by Response Evaluation Criteria in Solid Tumors (RECIST) * Prior chemotherapy with cabazitaxel and/or docetaxel is allowed but not required. If there has been prior chemotherapy, at least 2 weeks must have elapsed prior to leukapheresis * Prior radiotherapy is allowed provided it was not administered to the only evaluable site of disease and was \> 14 days prior to leukapheresis * No known contraindications to leukapheresis, steroids or tocilizumab * Total serum bilirubin =\< 2.0 mg/dL (to be performed within 42 days of signing the main study co…